120 Mr. A. Stephenson on the Forcing of 



must be included. The magnifying effect of the joint dis- 

 turbance depends upon the adjustment of the frequencies ; 

 and as the frequency of the free motion is a function of the 

 amplitude, the action can have appreciable effect in any 

 particular case only for a certain range of amplitude. 



6. The examination above brings oat the interesting fact 

 that when the system is sensitive to the disturbance the 

 oscillation generated is approximately of free period (under 

 variable spring) : thus a system of which the spring under- 

 goes periodic variation furnishes, in these cases, an exception 

 to the rule that forced vibrations follow the period of 

 the exciting cause. If a crowd of direct disturbances acts 

 on the system each in general produces a forced oscillation of 

 its own period ; but these elements are small in comparison 

 with the oscillations of approximately natural period gene- 

 rated by those disturbances to which the system is sensitive. 

 In this action, therefore, energy is given out by the system 

 in the period in which incident energy is most readily 

 absorbed. 



The phenomenon of fluorescence is the outstanding physical 

 case of a direct disturbance exciting an oscillation of different 

 period, and it has been shown that in glowdng sodium vapour 

 '• the fluorescence spectrum is the exact complement of the 

 absorption spectrum"*. Thus an assemblage of simple 

 systems of variable spring furnishes a mechanical analogue 

 to the vapour w T ith regard to fluorescence, at least in so far 

 as the main features are concerned. 



It is specially to be noted that the fluorescent spectrum 

 depends upon the frequency of the incident monochromatic 

 light ; this is in accordance with our analogy, for of the 

 assemblage of systems only a certain definite group is sensi- 

 tive to a disturbance of given frequency. From this point 

 of view, again, the lengthening and the shortening of the 

 period of the incident disturbance in emission are essentially 

 similar phenomena, and the exceptions to Stokes' law cease 

 to be exceptional. 



7. Owing to the counteracting influence of friction it is 

 difficult to realize more than a few cases of the joint action 

 in practice, but the effect may be observed readily in the two 



* "The Fluorescence and Absorption Spectra of Sodium Vapour," 

 by Prof. K. W. Wood and Mr. J. H. Moore; Phil. Mag. Sept. 1903. 

 Prof. Wood found subsequently, Phil. Mag. Nov. 1906, p. 499, on more 

 detailed examination that many absorption lines do not appear in the 

 fluorescent spectrum. In our analogue these would correspond to vibra- 

 tions of constant spring. It may be noted that the equidistance of the 

 lines of a group in the fluorescent spectrum produced by monochromatic 

 stimulation is in accordance with the properties of the mechanical system. 



